冗餘（Redundancy）或備援（Standby）機制可以提高給定系統之可靠度以及可用性。本文討論在連續生產的化工廠中，昂貴且須持續運轉的關鍵設備（如：泵、風扇、壓縮機及火炬塔等等）之建模及最適化。設備在長時間的操作過程中有可能會發生故障，也可能會須要滿足突然製程需求的變動，這些事件在本文中被統稱為「衝擊」(shock)。為了描述這些衝擊事件對設備結構的影響，我們建立兩類設備組態轉換規則，並引入了獨立齊次泊松過程 (Independent homogeneous Poisson Processes)，以利建構相對應數學規劃模型。本研究挑選化工廠中常見的兩種類型關鍵設備，即火炬塔(flare stack) 以及壓縮機(compressor)，進行深入的分析，並利用基因演算法來進行最適化計算，以最小化生命週期總預期支出，藉以決定出相應最合適的備援機制。從最適化結果可以得知：使用最少的暖備件將會造成較大的生命週期總支出，但相對來說建置成本會降低。總結來說，此次研究提供有效的方法來決定化工廠中各類關鍵元件的通用備援機制設計，平衡生命週期預期總支出和成本之間的關係。

In modern society, efficient resource management and allocation have become key factors for success across various industries. Whether in transportation, communication, manufacturing, or service sectors, dynamically allocating resources based on demand changes enhances operational efficiency greatly. For example, banks may adjust the number of service windows based on customer volume; ISPs (Internet Service Providers) may dynamically adjust bandwidth based on household user traffic demands; public transportation systems, such as buses, metros, and high-speed rails, may increase the number of services during peak hours. Beyond these everyday applications, the chemical plants also implement similar standby mechanisms. For instance, the reactors, pumps, compressors, and flare stacks may be operated in such a way to satisfy production needs. This manufactirung mode of dynamically adjusting resources based on demand changes is known as variable capacity resource management. By employing a rigorous mathematical programming model, an optimal allocation strategy can be generated to achieve efficient resource utilization and product production scheme. Mathematical programming models have been constructed in this study to generate the optimal standby mechanisms of two critical units in chemical plants, i.e., flare stacks and compressors. In the chemical plants, they represent two main catagories of stadbys. One is built to withstand only a single type of “shock,” such as the flare stacks adjusting solely on the basis of the volume of upstream waste gas; The other is configured according to mutiple types of “shocks,” such as the compressors can be operated in response to the downstream flow demand and outlet pressure changes. A series of case studies have been carried out in this study to demonstrate the correctness of the mathemetical models and, furthermore, via in-depth analysis of the model structure, it can be concluded that this work can be generalized to produce practical and feasible optimal standby schemes to enhance the operational efficiency and production flexibility of every chemical plant.

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